多水平随机中介效应估计及其比较

Comparisons of Estimation Methods for Multilevel Random Mediation Effect Model

本文在综述各类多水平中介模型的基础上,聚焦于自变量、中介变量、因变量都来自多水平结构中较低水平的多水平随机中介效应模型,通过蒙特卡洛模拟研究比较该模型与简化的多水平固定中介效应模型、传统中介效应模型的差别,并考察了目前用于多水平随机中介效应的三种参数估计方法:限制性极大似然、极大似然、最小方差二次无偏估计在不同情况下对随机中介效应估计的优劣。研究结果显示:当数据符合多水平随机中介效应模型时,使用简化模型将错误估计中介效应及其标准误,得到不正确的统计检验结果;使用多水平随机中介效应模型能够实现对中介效应的正确估计和检验,其中限制性极大似然或极大似然估计方法优于最小方差二次无偏估计方法。

The analysis of mediation effects is important in education, psychology, and other social sciences research. The approaches used in regression and path analysis for investigating such effects are widely known. These methods, however, are inappropriate if the data are clustered in nature, due to the violation of the assumption of independence of observations and biased standard errors. Therefore, a method for analyzing the mediation effects within multilevel models has been developed and proposed. Several procedures have been recommended and implemented in existing commercial software for testing of mediation effects in multilevel models. But most of these methods assumed that the effects are fixed, even for random indirect model. As a result, it is highly needed to examine the indirect effects under different conditions. There are few studies on this topic in Mainland till now. Following Bauer, Preacher, and Gil＇s （2006） study, the purpose of the present article focused on the multilevel random mediation effect model （1-1-1） and examined various analytical procedures for random multilevel meditation analysis. The performances of these procedures under different conditions were compared using Monte Carlo simulations method. First, in order to address why multilevel random mediation model is necessary, the improvement in using the random multilevel mediation model compared to two compact models, the multilevel fixed mediation model and the single-level traditional mediation model is examined. Second, three different estimation methods, restricted maximum likelihood estimate （REML）, maximum likelihood estimate （MLE）, and minimum variance quadratic unbiased estimate （MIVQUE） are compared in different conditions. The results indicate that we can obtain unbiased estimation of the mediation effect, correct standard error, and proper result of hypothesis test through using the multilevel random mediation model, comparing with using tke other two compact models. Moreover, the differences of multilevel fixed mediation model and single-level traditional mediation model are trivial. For the estimation random mediation effects in multilevel random mediation model, it is better to use restricted maximum likelihood estimate （REML） and maximum likelihood estimate （MLE）, comparing with minimum variance quadratic unbiased estimate （MIVQUE）. Only when the model has problem on converging, can one use MIVQUE instead, but researches should pay attention to the reliability of MIVQUE under different conditions. This paper consider the use of multilevel modeling to estimate mediation models in which there is lower level mediation, and all terms are random. It could be concluded that tests of random multilevel mediation can be problematic when more fixed effects models are used. For testing random indirect effects, different estimation methods might reach similar results. The REML method of SAS MIXED procedure is better than that of the MIVQUE method in the studied conditions. Recommendations are provided for testing multilevel mediation.